Transmission of radio signals, e.g. employed in a mobile communications environment such as GSM and UTMS systems, are subjected to reflections, dispersions and the like such that a plurality of sub-radio signals are transmitted to a receiver from different directions. In dependence of the phases, the received sub-signals amplify or reduce each other. Thus, the resulting received signal is a function varying with the location of the receiver and, in case of a moving receiver, varying in time. Additionally, a movement of a transmitter results in a frequency shift of received signals due to the Doppler effect.
In order to compensate frequency shifts and spreads of received radio signals, the so-called Doppler shift and Doppler spread are used to estimate a frequency shift and frequency spread. The Doppler shift is indicative of a frequency offset which characterizes the difference in mean frequency between transmitted and received signals. The Doppler spread is indicative of a frequency spread which characterizes in a multipath propagation environment how fast the transmission channel used for radio signals is fading.
The Doppler shift which is also referred to as Doppler frequency fd can be computed by:
                              f          d                =                              f            c                    ·                      v            c                                              (        1        )            wherein fc is the carrier frequency, v is the speed of a moving receiver (e.g. mobile user equipment such as a mobile telephone) and c is the speed of light.
As shown in FIG. 1, the two channel parameters, frequency offset and Doppler shift, characterize a Doppler spectrum of a wireless radio signal communications channel.
A mobile radio signal communications channel can be characterized by a sequence of complex channel coefficients varying in time:c(k)=Re{c(k)}+jIm{c(k)}  (2)
The channel coefficient sequence can be modeled as time discrete stationary random process wherein an autocorrelation sequence rcc(n) is defined as:
                                          r            cc                    ⁡                      (            n            )                          =                              lim                          K              →              ∞                                ⁢                                    1                                                2                  ⁢                  K                                +                1                                      ⁢                                                  ⁢                                          ∑                                  k                  =                                      -                    K                                                  K                            ⁢                                                                                          c                      _                                        *                                    ⁡                                      (                    k                    )                                                  ⁢                                                                  ⁢                                  c                  ⁡                                      (                                          k                      +                      n                                        )                                                                                                          (        3        )            
Transforming the autocorrelation sequence rcc(n) in the frequency domain, the respective power density spectrum φcc(f) is given by:
                                          ϕ            cc                    ⁡                      (            f            )                          =                              ∑                          n              =                              -                ∞                                      ∞                    ⁢                                                    φ                cc                            ⁡                              (                n                )                                      ⁢                                                  ⁢                          ⅇ                                                -                  2                                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                fTn                                                                        (        4        )            which describes the spectral distribution of an unmodulated signal transmitted over a mobile radio signal communications channel c. This power density function is also called Doppler power density spectrum the shape thereof being dependent of the environment wherein a moving party transmits or receives a radio signal and of its speed of movement.
In order to predict the shape of a Doppler power density spectrum, short Doppler spectrum, different modelling methods are employed. For example, for modelling a Doppler spectrum it is assumed that a radio signal from or to a mobile entity by means of a radio signal channel having only one direct line of sight to the mobile entity. For this easiest case, the Doppler spectrum can be denoted by:φccd(f)=δ(f−f0)  (5)wherein δ(f) denotes a dirac pulse. Here, the signal received by a mobile entity is simply shifted in frequency by a frequency offset.
A more complicated model assumes that radio signals are received or transmitted by a mobile entity by means of a channel for which no direct path is existing to the mobile entity. Thus, the resulting received signal comprises a superposition of signals received via indirect paths. In order to reduce the complexity of the calculation of a Doppler spectrum for the latter case, especially in case of a mobile radio signal communications environment, it is generally assumed that the propagation of signals takes place in a horizontal plane, that the angle of incidence is equally distributed in the range between 0 and 2π for all received signals and that the signal strengths for all signals via indirect paths are equally distributed. This assumption leads to the so-called Jake's spectrum which is given by:
                                          ϕ            cc            J                    ⁡                      (            f            )                          =                  {                                                                                                                2                      ⁢                                                                                          ⁢                                              σ                        0                        2                                                                                    π                      ⁢                                                                                          ⁢                                              f                        max                                            ⁢                                                                        1                          -                                                                                    (                                                              f                                /                                                                  f                                  max                                                                                            )                                                        2                                                                                                                                ,                                                                                                                      f                                                        ≤                                      f                    max                                                                                                                        0                  ,                                                                                                                      f                                                        >                                      f                    max                                                                                                          (        6        )            
On the basis of a Doppler spectrum according to equation (6), a Doppler frequency estimation method was proposed wherein, after a frequency offset compensation, an autocorrelation function for the Doppler spectrum is calculated, the autocorrelation function is expressed by a zero-order Bessel function of the first kind and the first-zero crossing of the autocorrelation function is determined. Further, this approach is performed on the basis of the slot rate used for the radio signals, wherein a slot is a duration which consists of fields containing information, e.g. bits. In particular, the slot rate based approach calculates a complex correlation function between so-called pilot bits or groups which usually serve as training signals. For obtaining an autocorrelation function, the sampling period is required to be much smaller than the inverse of the highest frequency expected in the Doppler spectrum. For example, the slot rate in an UMTS system is 1.500 Hz. Thus, it is impossible to perform a Doppler spread estimation on slot rate basis for frequencies above 750 Hz in an UMTS system.
Further, a Doppler spectrum according to equation (6) cannot be assumed under all circumstances depending on the communications environment, for example in rural areas compared with urban areas. Rather, Doppler spectra actually found in communications environments can be Gaussian distributed due to radio signal reflections and dispersions, can be defined by a dirac pulse due to a radio signal received via a channel having only one direct line of sight, can be result from a superposition of different distributions and combinations thereof.
For example, the above mentioned autocorrelation based approach using a Doppler spectrum according to equation (6) provides for ineffective Doppler spread estimation in case a line of direct sight component of received radio signals influences the resulting Doppler spectrum, e.g. by introducing a Doppler spectrum peak.
Object of the Invention
The object of the present invention is to overcome the above mentioned problems and in particular to provide a solution for a Doppler spread estimation when the autocorrelation function of a Doppler spread deviates from a Bessel function due to the existence of a line of sight component.
Solution According to the Invention
The present invention teaches to use a definition for the Doppler spread of a received radio signal in the time domain. In particular, a Doppler spread definition is used wherein the Doppler spread is characterized by a function in-time of an autocorrelation function of a received radio signal and the first and second derivatives of the autocorrelation function.
For an estimation of the Doppler spread of a radio signal on the basis of such a definition, the basic idea underlying the present invention is to estimate the first and second derivatives of the autocorrelation function determined for the radio signal for a predefined point of time.
For an determination of the autocorrelation function and its first and second derivatives, an autocorrelation sequence is defined for the radio signal by modeling the signal as a time discrete signal. In particular, the autocorrelation sequence is determined for known signal portions of the received radio signal such as training sequence signals or so-called pilot symbols.
On the basis of discrete autocorrelation coefficients for the autocorrelation sequence, the first and second derivatives of the autocorrelation function are estimated. In order to reduce or eliminate disturbances of the radio signal due to signal noise, it is contemplated to employ specific autocorrelation coefficients for the estimation of the first and second derivatives.
For estimating the Doppler spread, the values for the autocorrelation function obtained from the autocorrelation coefficients and the estimations based thereon are used to evaluate the Doppler spread definition.
With respect to a mobile telephone system, such as a GSM or UTMS environment, the basic idea underlying the present invention can be defined as a calculation or estimation of Doppler spread for radio signals transmitted according to the respective communications standards on the basis of an autocorrelation function of received and demodulated training or pilot signal of a control channel.
Short Description of the Invention
In a greater detail, the present invention provides a method for Doppler spread estimation for a radio signal transmission channel in a mobile communications environment on the basis of a radio signal transmitted via the transmission channel. For carrying out the method according to the invention an autocorrelation function for the radio signal is determined and a Doppler spread for the radio signal is defined as a function in time of the autocorrelation function and its first and second derivatives for a point of time being zero. While the autocorrelation function for the point of time being zero is determined, the first and second derivates of the autocorrelation function are estimated for the point of time being zero. In particular, this estimations are obtained by an averaging of respective portions of the autocorrelation function each thereof including the point of time being zero. The determined and estimated values for the autocorrelation function are used to compute the defined Doppler spread function whereby an estimated value for the Doppler spread is obtained.
For the determination of the autocorrelation function it is possible to model the radio signal as a time discrete signal and to determine an autocorrelation sequence for the time discrete signal representing the transmitted radio signal.
For the determination and estimation of values of the autocorrelation function it is possible to calculate autocorrelation coefficients for the autocorrelation sequence. Optionally it is contemplated to define a correlation influence length and to determine autocorrelation sequence coefficients by means of a recursive function.
For obtaining the recursive function used for the determination of autocorrelation sequence coefficients, a linear or an exponential averaging of the autocorrelation sequence is possible.
An estimation of the first and second derivatives of the autocorrelation function can be provided by determining respective slopes of the autocorrelation function wherein the estimation for the second derivatives of the autocorrelation function which can be considered as a respective slope of the first derivative of the autocorrelation function can also be calculated on the basis of slopes of the autocorrelation function itself.
In the case of an autocorrelation sequence, slopes of the autocorrelation function can be determined by averaging processes for respective autocorrelation coefficients. In particular, two autocorrelation coefficients for points of time, which define a time interval including the point of time (t=0) for which the first and second derivatives of the autocorrelation function are to be estimated, are chosen. By means of a linear averaging of two autocorrelation coefficients chosen in this manner the slopes of the autocorrelation function are respectively determined. Preferably the determination of each slope of the autocorrelation function is performed such that only two values of the autocorrelation function are necessary to estimate the first and second derivatives thereof. As a result, the estimation of the Doppler spread for the transmission channel can be performed on the basis of only two values for the autocorrelation function defined for the radio signal.
In order to reduce disturbances of the radio signal due to signal noise possible leading to an estimation error for the Doppler spread, it is contemplated to only use such portions of the autocorrelation function for the estimation of the first and second derivatives thereof which are not affected by signal noise.
Especially such a noise resistant estimation of the Doppler spread can be accomplished if values for the autocorrelation function are employed which do not include autocorrelation function values for the point of time being zero. Further, it is possible to use single, discrete autocorrelation coefficients forming parts of the autocorrelation sequence to estimate the first and second derivatives of the autocorrelation function. In particular, such a procedure is preferred in the case of modeling the radio signal as a time discrete signal.
Using discrete autocorrelation coefficients for the estimation of the first and second derivatives of the autocorrelation function, only two autocorrelation coefficients can be utilized wherein it is possible to determine at least one of the used autocorrelation coefficients in dependence of the correlation influence length defined for the autocorrelation function of the autocorrelation sequence, respectively.
Further optimization for the estimation of the Doppler spread can be obtained by evaluating the signal to noise ratio expected for the estimated second derivative of the autocorrelation function. In view of a threshold value defined for a signal to noise ratio, the signal to noise ratio for the estimated second derivative of the autocorrelation function is determined for different autocorrelation coefficients of the autocorrelation sequence. In the case no autocorrelation coefficients leads to a signal to noise ratio for the estimated second derivative of the autocorrelation function below the predefined signal to noise ratio threshold value, the Doppler spread is estimated to be zero. The same estimation for the Doppler spread can result if further constraints are defined in dependence of the autocorrelation coefficients with respect to the estimated second derivative of the autocorrelation function. An estimation of the Doppler spread as described above can be performed if, in particular, the signal to noise ratio for the estimated second derivative of the autocorrelation function exceeds the defined signal to noise ratio threshold value for a specific autocorrelation coefficient. Then, this autocorrelation coefficient is used for the estimation of the second derivative of the autocorrelation function.
In dependence of the manner the radio signal is transmitted via the transmission channel, it is possible, after having received the radio signal, to demodulate the received radio signal in particular in view of a predefined signal sequence included in the radio signal. Here, the autocorrelation function is determined as an autocorrelation function for the demodulated radio signal.
In a similar manner as described above, it is possible to define an autocorrelation sequence for the demodulated radio signal.
Especially in the case the radio signal includes, beside the predefined signal sequence, further signal portions it is contemplated to define the autocorrelation sequence and, in particular, the autocorrelation sequence for demodulated radio signal portions being indicative of the predefined signal sequence. This can be accomplished by means of a recursive function defining a relation between autocorrelation coefficients of the autocorrelation sequence. Such a recursive determination of autocorrelation coefficients can include averaging processes for the autocorrelation sequence, in particular in view of the percentage of the predefined signal sequence portion in the demodulated radio signal.
As a preferred embodiment, the present invention is utilized in a mobile telephone environment such as a GSM or UTMS system. Here, the transmission channel for which the Doppler spread is to be estimated can be a control channel such as a DPCCH channel. According to the standards of such mobile telephone environments, the radio signal used for a Doppler spread estimation comprises at least one frame having subsequent slots each thereof including a number of predefined pilot symbols. In this case, the predefined pilot symbols represent the above predefined signal sequence. By demodulating the radio signal it is possible to obtain the demodulated pilot symbols per slot for which autocorrelation coefficients can be determined. On the basis of the autocorrelation coefficients obtained for the demodulated pilot symbols, the first and second derivatives of the autocorrelation function can be estimated which are, in turn, used to estimate the Doppler spread.
Further, the present invention provides a computer program product for carrying out the above described methods and a receiver for a mobile communications environment being adapted to incorporate the above described methods.